Bar complexes and extensions of classical exponential functors

Antoine Touzé[1]

  • [1] Université Paris 13 Sorbonne Paris Cité, LAGA, CNRS, UMR 7539, F-93430, Villetaneuse (France)

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 6, page 2563-2637
  • ISSN: 0373-0956

Abstract

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We compute Ext-groups between classical exponential functors (i.e. symmetric, exterior or divided powers) and their Frobenius twists. Our method relies on bar constructions, and bridges these Ext-groups with the homology of Eilenberg-Mac Lane spaces.This article completes earlier results of the author, and provides an alternative approach to classical Ext-computations in the category of strict polynomial functors over fields. We also obtain significant Ext-computations for strict polynomial functors over the integers.

How to cite

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Touzé, Antoine. "Bar complexes and extensions of classical exponential functors." Annales de l’institut Fourier 64.6 (2014): 2563-2637. <http://eudml.org/doc/275421>.

@article{Touzé2014,
abstract = {We compute Ext-groups between classical exponential functors (i.e. symmetric, exterior or divided powers) and their Frobenius twists. Our method relies on bar constructions, and bridges these Ext-groups with the homology of Eilenberg-Mac Lane spaces.This article completes earlier results of the author, and provides an alternative approach to classical Ext-computations in the category of strict polynomial functors over fields. We also obtain significant Ext-computations for strict polynomial functors over the integers.},
affiliation = {Université Paris 13 Sorbonne Paris Cité, LAGA, CNRS, UMR 7539, F-93430, Villetaneuse (France)},
author = {Touzé, Antoine},
journal = {Annales de l’institut Fourier},
keywords = {Strict polynomial functors; extensions; bar complexes; Eilenberg-Mac Lane spaces; Frobenius twist; exponential functors; strict polynomial functors; bar construction; symmetric algebra; exterior algebra; divided power algebra},
language = {eng},
number = {6},
pages = {2563-2637},
publisher = {Association des Annales de l’institut Fourier},
title = {Bar complexes and extensions of classical exponential functors},
url = {http://eudml.org/doc/275421},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Touzé, Antoine
TI - Bar complexes and extensions of classical exponential functors
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 6
SP - 2563
EP - 2637
AB - We compute Ext-groups between classical exponential functors (i.e. symmetric, exterior or divided powers) and their Frobenius twists. Our method relies on bar constructions, and bridges these Ext-groups with the homology of Eilenberg-Mac Lane spaces.This article completes earlier results of the author, and provides an alternative approach to classical Ext-computations in the category of strict polynomial functors over fields. We also obtain significant Ext-computations for strict polynomial functors over the integers.
LA - eng
KW - Strict polynomial functors; extensions; bar complexes; Eilenberg-Mac Lane spaces; Frobenius twist; exponential functors; strict polynomial functors; bar construction; symmetric algebra; exterior algebra; divided power algebra
UR - http://eudml.org/doc/275421
ER -

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